The title of Stephen Frears' new docudrama, which debuts on HBO on Saturday, is obviously provocative: "Muhammad Ali's Greatest Fight." It could refer to many things — his bouts in the boxing ring, his complicated relationship with the public or even his battle against Parkinson's.

But what probably doesn't leap to mind is a behind-the-scenes look at the Supreme Court case Clay vs. the United States. And with good reason.

Drafted in 1967, the heavyweight boxing champion and newly converted Muslim refused to participate in the Vietnam War. No longer known by his former name of Cassius Clay, Ali explained that the Koran would not allow him to take up arms unless instructed by Allah.

He was charged with draft dodging, stripped of his title, kicked out of boxing, fined $10,000 and arrested. His appeal worked its way up to the Supreme Court. Which is where "Muhammad Ali's Greatest Fight" begins.

If you're expecting impassioned court scenes involving Ali and his lawyers or dramatizations of how he coped with everything, well, that is not how this film works. Frears has chosen to show the fighter through news clips, which provide some of the most exciting moments in the film (not to mention a rather different discussion around Islam than we are currently having.)

Ali has become so mythologized that it's easy to forget why. Yes, he was a gifted athlete who recited funny poems, but he was also a lyrical, passionate and surprisingly self-controlled advocate for black power and civil rights. So he was not someone who would obviously impress the conservative majority of the Supreme Court at the time.

We meet the nine justices through the eyes of Kevin Connolly (Benjamin Walker), just hired by Christopher Plummer's Justice John Harlan II, who is the focus of the film. A dashing, decent and ailing man who has long supported Chief Justice Warren E. Burger (Frank Langella), Harlan still prizes law over politics.

That tension — the purity of the legal process versus the realities of Washington — is just one of many at work. Racism, the shifting attitudes toward the war, questions of loyalty and the simple power of personality come together in this slow and steady look at how Clay vs. the United States was resolved.

Despite its incendiary title, "Muhammad Ali's Greatest Fight" deals almost exclusively in subtleties. The division between liberals and conservatives on the court are clear — the liberals, including William Brennan Jr. (Peter Gerety), Thurgood Marshall (Danny Glover) and Hugo Black (Fritz Weaver), are the ones who finally agree to hear Ali's case (Marshall had to recuse himself since he was U.S. solicitor general when the case began).

But the argument for overturning Ali's conviction has nothing to do with politics or personality. Instead, it had everything to do with the legal fine print, which makes the film's climax more muted than you might hope. It is also undeniably odd to see a film about Ali peopled almost exclusively by white men. But that is the point too — these are the architects and guardians of the system.

The cast, led by Plummer and Langella, is so fabulous you might find yourself wondering if it isn't time for a dramatic series revolving around this Supreme Court. The guy playing Justice Potter Stewart seems so comfortable with legal diplomacy, you might wonder if he's actually a lawyer — nope, just film director Barry Levinson in really great specs.

But there is a gap between the men of the court and the man behind the case that the film cannot close. As interesting and semi-admirable as the decision-making process may have been, it's hard to forget who's standing in the wings. Ali took a highly controversial stand in front of the world and willingly suffered the consequences. The legal wrangling of eight old white men behind closed doors simply pales in comparison.

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